A fast-moving, high-impact nor'easter lashed the Massachusetts south shore and Cape Cod Saturday night with near hurricane-force winds and impressive snow totals, but spared much of the rest of the state.

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Snow fell at rates of 2 to 3 inches an hour in the jackpot areas of the Upper Cape and south shore, and high winds led to power outages which left over 20,000 customers in the dark during the storm.

In advance of the storm, Gov. Deval Patrick asked all residents of eastern Massachusetts to stay off the highways.

"At the height of the storm, it won't be possible to keep up with the clearing of the roads," Patrick said at a Saturday afternoon news conference. He asked residents who live east of Marlborough, which is all of eastern Massachusetts inside Route 495, to stay off the roads between 5 p.m. Saturday and 5 a.m. Sunday.

Massachusetts State Police followed with a terse "Stay in tonight" warning on its Twitter feed.

For much of eastern Massachusetts, the storm was a nuisance, but for southeastern areas and Cape Cod, it was a very different story.

Snowfall totals ranged from 15.5 inches in Sandwich and 10.5 inches in Yarmouth to less than 2 inches in Ipswich, north of Boston.

The National Weather Service issued a blizzard warning for coastal Essex County, Cape Cod and the Islands and Plymouth County from Saturday afternoon through Sunday morning. For Cape residents, it was their third blizzard warning of the winter.

Boston was largely spared any significant impact from the storm, with just over three-and-a-half inches reported at Logan Airport. Mayor Marty Walsh had elected not to declare a snow emergency in the city.

Massport said most domestic airlines had limited operations at Logan Saturday evening and night.

Another storm is in the forecast for Tuesday, with perhaps 1 to 3 inches of snow expected.